We will first review the McKay correspondence and its generalization using elementary group theory. It gives a 1-1 correspondence between finite subgroups of SL(2, C) and simply laced affine Dynkin diagrams. We use group theoretical data to construct the basic representations of simply laced toroidal Lie algebras, which contain affine Lie algebras as distonguished subalgebras.

Speaker's profile: Jing Naihuan is a professor at North Carolina State University in the United States. Has received honors such as the National Overseas Outstanding Youth Fund, Humboldt Research Fund in Germany, and Fulbright Scholar in the United States. I have taught or conducted research at institutions such as Princeton Institute for Advanced Study, University of Michigan, and University of Kansas in the United States. As a visiting professor or researcher, I have visited renowned mathematics centers such as the Berkeley Mathematics Institute in the United States, the Max Planck Institute for Mathematics in Bonn, Germany, and the Max Planck Institute for Applied Mathematics in Leipzig, Germany multiple times. My main research directions include infinite dimensional Lie algebras, quantum groups, vertex operator algebras, algebraic combinations, and quantum computing.